Solve the followi

Ideas required to solve the problem:

The general solution of any trigonometric equation is given as –

• sin x = sin y, implies x = nπ + (– 1)ⁿy, where n ∈ Z.

• cos x = cos y, implies x = 2nπ ± y, where n ∈ Z.

• tan x = tan y, implies x = nπ + y, where n ∈ Z.

given,

tan x + tan 3x = 2tan 2x

⇒ tan x + tan 3x = tan 2x + tan 2x

⇒ tan 3x – tan 2x = tan 2x – tan x

⇒

As, tan (A - B) =

∴

⇒

⇒

∴ tan x = 0 or tan 2x = 0 or tan 3x = tan x

if tan x = tan y, implies x = nπ + y, where n ∈ Z

∴ x = nπ or 2x = mπ or 3x = kπ + x

∴

∴